Mastering Polynomial Addition: A Step-by-Step Guide

Algebra 2 Grades High School 6:38 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to add polynomials by combining like terms, understanding exponent rules, and organizing your work for accuracy. This lesson is designed for Algebra 2 students and covers essential techniques for polynomial manipulation.

Video Resource

Polynomial Addition Algebra

Kevinmathscience

Duration: 6:38
Watch on YouTube

Key Concepts

  • Polynomial
  • Like Terms
  • Exponents
  • Combining Like Terms
  • Descending/Ascending Order

Learning Objectives

  • Students will be able to identify like terms in polynomial expressions.
  • Students will be able to add polynomial expressions by combining like terms.
  • Students will be able to write polynomials in descending or ascending order.

Educator Instructions

  • Introduction (5 mins)
    Begin by briefly reviewing what a polynomial is and the definition of a term. Briefly review exponents. Introduce the concept of 'like terms' – terms with the same variable raised to the same power. Explain that this lesson will focus on adding polynomials by combining these like terms, similar to combining 'apples with apples'.
  • Video Viewing and Note-Taking (10 mins)
    Play the Kevinmathscience video 'Polynomial Addition Algebra'. Instruct students to take notes on the key steps outlined in the video, paying attention to how like terms are identified and combined. Encourage them to note the importance of keeping exponents consistent when adding like terms.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video. Start with simpler examples and gradually increase complexity, including examples with multiple variables and negative coefficients. Emphasize the importance of careful organization and checking work.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of polynomial addition problems. Encourage them to use the techniques learned in the video and during guided practice. Circulate to provide assistance and answer questions.
  • Wrap-up and Discussion (5 mins)
    Review the key concepts of polynomial addition. Address any remaining questions or misconceptions. Preview the next lesson, which might cover polynomial subtraction or multiplication.

Interactive Exercises

  • Term Identification Game
    Present a polynomial expression and have students identify all the like terms. This can be done as a class or in small groups, with students earning points for correct identifications.
  • Polynomial Addition Relay Race
    Divide the class into teams. Each team receives a set of polynomial addition problems. Students take turns solving one problem at a time, passing the paper to the next teammate. The first team to correctly solve all problems wins.

Discussion Questions

  • Why is it important to only combine 'like terms' when adding polynomials?
  • What are some strategies you can use to avoid mistakes when adding polynomials, especially with negative coefficients?
  • How does the order of terms in a polynomial affect its value?

Skills Developed

  • Algebraic manipulation
  • Attention to detail
  • Problem-solving
  • Organization
  • Critical thinking

Multiple Choice Questions

Question 1:

Which of the following terms can be combined with 3x²y?

Correct Answer: -2x²y

Question 2:

What is the sum of (5a³ + 2a - 1) and (2a³ - a + 4)?

Correct Answer: 7a³ + a + 3

Question 3:

Simplify: (4x² - 2x + 1) + (x² + 5x - 3)

Correct Answer: 5x² + 3x - 2

Question 4:

Which expression represents the sum of (2b⁴ - 3b² + 5) and (b⁴ + b² - 2)?

Correct Answer: 3b⁴ - 2b² + 3

Question 5:

What is the result of adding (6y³ + 4y - 2) and (-2y³ + y² + 3)?

Correct Answer: 4y³ + y² + 4y + 1

Question 6:

What is the sum of (7p⁴ + 3p² - 2) and (2p⁴ - p² + 5)?

Correct Answer: 9p⁴ + 2p² + 3

Question 7:

Simplify: (5x² + 4xy - 2y²) + (2x² - xy + 3y²)

Correct Answer: 7x² + 3xy + y²

Question 8:

What is the result of adding (8a³ - 5a + 2) and (-3a³ + 2a² - 1)?

Correct Answer: 5a³ + 2a² - 5a + 1

Question 9:

Which expression represents the sum of (4m⁵ - 2m³ + m) and (m⁵ + 3m³ - 2m)?

Correct Answer: 5m⁵ + m³ - m

Question 10:

What is the sum of (9b² - 6b + 3) and (-4b² + 2b - 5)?

Correct Answer: 5b² - 4b - 2

Fill in the Blank Questions

Question 1:

When adding polynomials, you can only combine __________ __________.

Correct Answer: like terms

Question 2:

The __________ of the variable must be the same to combine terms.

Correct Answer: exponent

Question 3:

The sum of 3x² + 2x and 5x² - x is __________.

Correct Answer: 8x² + x

Question 4:

When simplifying (4y³ - y + 2) + (2y³ + 3y - 1), the resulting polynomial is __________.

Correct Answer: 6y³ + 2y + 1

Question 5:

The simplified form of (a⁴ - 2a² + 1) + (3a² - 4) is __________.

Correct Answer: a⁴ + a² - 3

Question 6:

The sum of (6m³ + 4m - 3) and (-2m³ + m² + 5) is __________.

Correct Answer: 4m³ + m² + 4m + 2

Question 7:

When simplifying (5x² + 3xy - 2y²) + (2x² - xy + 3y²), the resulting polynomial is __________.

Correct Answer: 7x² + 2xy + y²

Question 8:

The simplified form of (8b³ - 5b + 2) + (-3b³ + 2b² - 1) is __________.

Correct Answer: 5b³ + 2b² - 5b + 1

Question 9:

The sum of (4p⁵ - 2p³ + p) and (p⁵ + 3p³ - 2p) is __________.

Correct Answer: 5p⁵ + p³ - p

Question 10:

When simplifying (9a² - 6a + 3) + (-4a² + 2a - 5), the resulting polynomial is __________.

Correct Answer: 5a² - 4a - 2

Educational Standards

A2.A.2.2:Add, subtract, multiply, divide, and simplify polynomial expressions.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans